Geometric information and rational parametrization of nonsingular cubic blending surfaces
type: Item
instance of: scholarly article
title: Geometric information and rational parametrization of nonsingular cubic blending surfaces
zbMATH Open document ID: 1358.65016
DOI: 10.1155/2011/349315
author: Minghao Guo
author: Tieru Wu
author: Shugong Zhang
published in: Journal of Applied Mathematics
publication date: 2011-10-27T00:00:00Z
review text: Summary: The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be \(F_3, F_4\), or \(F_5\) surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by \textit{T. G. Berry} and \textit{R. R. Patterson} in [Comput. Aided Geom. Des. 18, No. 8, 723--738 (2001; Zbl 0983.68221)], we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 5964437
Wikidata QID: Q58690322
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/349315
OpenAlex ID: W2061326602
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DBLP publication ID: journals/jam/GuoWZ11
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description: scientific article; zbMATH DE number 5964437